A language lexicon can be divided into four main strata, depending on origin of words: core vocabulary words, fully- and partially-assimilated foreign words, and unassimilated foreign words (or transliterations). This paper focuses on translation of fully- and partially-assimilated foreign words, called "borrowed words". Borrowed words (or loanwords) are content words found in all languages, occupying up to 70% of the vocabulary. We use models of lexical borrowing in machine translation as a pivoting mechanism to obtain translations of out-of-vocabulary loanwords in a low-resource language. Our framework obtains substantial improvements (up to 1.6 BLEU) over standard baselines.